Name: ___________________________________________ Date: _____________________________
BLM 1–1
Chapter 1 Self-Assessment
Concept
BEFORE
DURING
(What I can do)
AFTER
(Proof that
I can do this)
1.1
I can write a formula to determine
the general term of an arithmetic
sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can generate a sequence that
represents a particular situation.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can provide an example of an
arithmetic sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can justify an example of an
arithmetic sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can derive a rule for determining
the general term of an arithmetic
sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can determine t1, d, n, or tn in a
problem that involves an arithmetic
sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can describe the relationship
between an arithmetic sequence
and a linear function.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can solve a problem that involves
an arithmetic sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
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Name: ___________________________________________ Date: _____________________________
BLM 1–1
(continued)
Concept
BEFORE
DURING
(What I can do)
AFTER
(Proof that
I can do this)
1.2
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can derive a rule for determining ‰ No, not yet
the sum of n terms of an
‰ Some
arithmetic series.
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can determine t1, d, n, or Sn in an
arithmetic series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can solve a problem that
involves an arithmetic series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can provide an example of a
geometric sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can justify an example of a
geometric sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can determine the values of t1, r,
or tn in a problem that involves a
geometric sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can derive a rule for determining ‰ No, not yet
the general term of a geometric
‰ Some
sequence.
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can determine the sum of an
arithmetic series.
1.3
I can solve a problem that
involves a geometric sequence.
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BLM 1–1
(continued)
Concept
BEFORE
DURING
(What I can do)
AFTER
(Proof that
I can do this)
1.4
I can derive a rule for determining ‰ No, not yet
the sum of n terms of a geometric ‰ Some
series.
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can determine t1, r, n, and Sn in
a geometric sequence.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can solve a problem that
involves a geometric series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can identify any assumptions
made when identifying a
geometric series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can solve a finance problem
using a geometric series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can write a repeating decimal
as the sum of an infinite
geometric series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can generalize a rule for
determining the sum of an
infinite geometric series.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can explain why a geometric
series is convergent.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
I can explain why a geometric
series is divergent.
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
‰ No, not yet
‰ Some
‰ Yes
1.5
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Name: ___________________________________________ Date: _____________________________
BLM 1–2
Chapter 1 Prerequisite Skills
1. Determine whether each relation is linear or
non-linear. Justify each answer.
a) A = πr 2
b) y = 5x – 3
c) (0, 0), (1, 1), (4, 2), (9, 3), (16, 4)
d) (2, 5), (4, 10), (6, 15), (8, 20), (10, 25)
2. Christina writes the following number
pattern: 9, 16, 23, … .
a) Create a table of values for the first
five terms.
b) Develop an equation that can be used to
determine the value of each term in the
number pattern.
c) What is the value of the 71st term?
d) Which term has a value of 135?
3. Julian creates a number pattern that starts
with the number −4. Each subsequent term
is 5 less than the previous term.
a) Create a table of values for the first five
numbers in the pattern.
b) What equation can be used to represent
the pattern? Verify your answer
by substituting a known value into
your equation.
c) What is the value of the 49th term?
d) Which term has a value of −89?
4. Create a graph and a linear equation to
represent each table of values.
a)
b)
x
y
–3
–8
–2
–5
–1
–2
0
1
1
4
2
7
3
10
x
y
12
2
15
3
18
4
21
5
24
6
27
7
30
8
5. Express each equation in slope-intercept
form.
a) 2x + y = 6
b) 3x + y + 9 = 0
c) 5x + 6y = 8
d) 6x – y = 4
e) 7x – y + 9 = 0
f) 8x – 4y = 3
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Name: ___________________________________________ Date: _____________________________
BLM 1–2
(continued)
6. What is the value of each expression?
a) 53
b) (−6)4
⎛1⎞
c) ⎜ ⎟
⎝2⎠
4
⎛ 2⎞
d) ⎜ − ⎟
⎝ 3⎠
2
a) Create a table of values showing the
amount of protactinium remaining
after the first five 2-min intervals.
b) How long would it take for the sample to
1
be reduced to
th its original size?
64
7. Evaluate.
a)
3
−8
b) 4 81
⎛1⎞
⎜ ⎟
⎝9⎠
c)
d)
9. Protactinium has a half-life of 2 min.
Suppose a sample of protactinium has a
mass of 1000 g. The formula for the mass
of protactinium remaining after n 2-min
n
⎛1⎞
intervals is A = 1000 ⎜ ⎟ .
⎝2⎠
5
⎛ 32 ⎞
⎜−
⎟
⎝ 243 ⎠
8. Simplify each expression by rewriting it
using positive exponents only.
123
127
1
b) 2 −3
st
8t
c) −3
t
a)
( )
d) ⎡ xy 5
⎣⎢
−3
⎤
⎦⎥
−2
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BLM 1–3
Chapter 1 Warm-Up
Section 1.1 Warm-Up
1. Describe the pattern demonstrated by each
of the following.
a) 2, 4, 6, 8, …
b) 1, 4, 7, 10, …
c) 5, 11, 17, …
2. Solve for x.
a) 35 = 3x – 4
b) 64 = –2(x – 3)
3. If g(n) = 6n – 11, determine
a) g(1)
b) g(0)
c) g(–3)
4. For each system of linear equations, use
elimination or addition to solve for x.
a) 22 = 2x – y
12 + 2x = 3y
1
1
b) 7 = x + y
2
2
–10 – x = 2y
5. Consider the equation y = 4x – 1.
a) Determine the slope and y-intercept of
the line.
b) Create a table of values for values of x
from 0 to 5.
Section 1.2 Warm-Up
1. Identify whether each of the following is an
arithmetic sequence. If so, state the values
of t1 and d.
a) 2, 4, 6, …
b) –5, 10, –20 …
c) 1, 4, 7, …
d) –6, –1, 4, …
4. Solve the following linear system for x
and y.
2y – 3x = 5 and 3y = –5x + 1
5. Copy each diagram into your notebook
and sketch the resulting rotations about the
point C.
a)
2. For tn = t1 + (n – 1)d,
a) explain the meaning of tn, t1, n, and d
b) determine t26 for 3, 6, 9, …
c) determine t1 if t30 = 82 and d = 3
d) write the general form for 2, 6, 10, …
3. Simplify each equation.
a) y = 2[3(x – 1) + 3]
1
b) y = [4(x + 2) – 6]
2
2
c) y = (27 + 54x)
3
b)
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BLM 1–3
(continued)
Section 1.3 Warm-Up
1. Determine whether each pattern represents
an arithmetic sequence. If it does, state the
value of t1 and d. If it does not represent an
arithmetic sequence, explain why.
a) 2, 4, 6, …
b) 2, 4, 8, …
c) 5, 3, 1, …
d) –4, –2, –1, …
4. Use technology to determine each value to
the nearest hundredth.
2. For the arithmetic sequence –6, –3, 0, …,
a) what is the general term tn?
b) determine S10.
5. a) Using elimination, solve for r in the
following system.
4r + s = 10
2r + s = –44
b) Using substitution, solve for r in the
following system.
4
s= r
3
3s + r = 256
3. A 20 cm × 16 cm photograph of a company
logo is being used for advertisements.
Determine the new dimensions if the
photograph needs to be
a) enlarged 240% to create a poster.
b) reduced by 25% to fit in a book.
a)
3
45
b) 7 16
c)
25
28 712
d) 3 125 =
3
s
7
Section 1.4 Warm-Up
1. Determine whether each sequence is
arithmetic, geometric, or neither.
a) 0.6, 0.66, 0.666, …
b) 5, 6, 7, …
c) 4, –4, 4, …
1 1 1
d) ,
,
, ...
4 16 64
17 12 7
e)
,
, , ...
5 5 5
2. For each sequence,
• determine r.
• write the next two terms.
• determine the general term tn.
a) 2, –6, 18, …
−10 20 −40
b) 5,
,
,
, ...
3
9
27
3. What is n in the sequence
2, 14, 98, " , 4802? Justify your work.
4. What is r in each of the following?
1
a) 125 = r 4
5
1 1
1
b) 1, ,
, ",
6 36
7776
5. If t2 = 28 and t5 = 1792, what are the values
of t1, r, and tn?
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BLM 1–3
(continued)
Section 1.5 Warm-Up
1. Identify whether each series is arithmetic
or geometric. Then, determine S18 to the
nearest tenth, if appropriate.
5
a) 3 + + 2 + ...
2
3
3
b) 3 + + + ...
2
4
c) 10 + 13 + 16 + …
d) 12 + 24 + 48 + …
2. Consider the series
1 1 1
1
.
1− + −
+" +
3 9 27
59 049
a) Determine t1, r, and n.
b) Write the general form for tn.
c) Determine the sum of the series,
to the nearest hundredth.
3. Draw a 6 cm line and label the endpoints A
and B. Locate the midpoint between
points A and B and label it C. Locate the
midopoint between points A and C and label
it D. Suppose this process continues with
points E and F, respectively.
a) Write a sequence that represents the
process.
b) If the next point is included, determine
the length of segment AG.
4. Write each fraction as a repeating decimal.
2
a)
9
23
b)
99
47
c)
999
5. Simplify. Express each answer in fraction
form.
3⎛
4⎞
a) ⎜ 2 − ⎟
4⎝
5⎠
2
2⎛
1⎞
b) − ⎜1 + ⎟
5⎝
6⎠
3
6. Evaluate. Express each answer to the
nearest hundredth.
⎛1⎞
a) ⎜ ⎟
⎝2⎠
4
⎛1⎞
b) ⎜ ⎟
⎝2⎠
6
⎛1⎞
c) ⎜ ⎟
⎝2⎠
8
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BLM 1–4
Section 1.1 Extra Practice
1. Identify which of the following sequences
are arithmetic. For each arithmetic
sequence, state the values of t1 and d,
and the next three terms.
a) 4, 7, 10, 13, …
b) 12, 7, 2, –3, …
c) 5, 15, 45, 135, …
d) x, x2, x3, x4, …
e) x, x + 2, x + 4, x + 6, …
2. Write the first four terms of each arithmetic
sequence for the given values of t1 and d.
a) t1 = –5, d = –2
b) t1 = 10, d = –0.5
c) t1 = 3, d = x
7
1
d) t1 = , d =
3
3
3. Given the general term, state the first four
terms of each sequence. Then, graph tn
versus n.
a) tn = 13 – 3n
1
b) tn = n + 4
2
4. Determine the general term and the 50th
term for each arithmetic sequence.
a) 6, 10, 14, …
b) 3, 2 1 , 2, …
2
5. Determine the number of terms in each
finite arithmetic sequence.
a) –6, –3, 0, …, 222
b) 3 1 , 3 3 , 4 1 , … , 15 3
4
4
4
4
6. Determine the unknown terms in each
arithmetic sequence.
a) 4, …, …, 16
b) …, 8, …, …, 2
c) 20, …, …, …, …, –10
7. The 20th term of an arithmetic sequence is
107, and the common difference is 5.
Determine the first term, the general term,
and the 40th term of this sequence.
8. Use the two given terms to find t1, d, and tn
for each arithmetic sequence.
a) t11 = 25, t30 = 101
b) t2 = 90, t51 = –57
9. The terms 5 + x, 8, and 1 + 2x are
consecutive terms in an arithmetic sequence.
Determine the value of x and state the
three terms.
10. The triangular shapes are made from
asterisks.
a) How many asterisks will be in the fourth
triangle? the fifth triangle?
b) Write the general term for the sequence
involving the number of asterisks in the
triangles.
c) How many asterisks will be in the
20th diagram?
d) Which diagram will contain
126 asterisks?
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BLM 1–5
Section 1.2 Extra Practice
1. Determine the sum of each arithmetic series.
a) 14 + 10 + 6 + " + (–86)
b) 5 + 6.5 + 8 + " + 26
c)
3
13
49
+2+
+"+
4
4
2
2. For each arithmetic series, determine the
indicated sum.
a) 4 + 9 + 14 + …; first 12 terms
b) (–16) + (–14) + (–12) + …; first 17 terms
c) x + 3x + 5x + …; first 20 terms
3. For each arithmetic series, determine the
number of terms.
a) 3 + 7 + 11 + " + tn = 465
b) –2 – 5 – 8 – " – tn = –950
c) t1 = 20, tn = –40, Sn = –210
4. For each arithmetic series, determine the
12th term and the 12th partial sum.
a) 3 – 1 – 5 – …
3
7 11
b) + +
+…
5
5
5
6. Determine the sum of all multiples of 7
between 1 and 1000.
7. In an arithmetic series, the third term is 24
and the sixth term is 51. What is the sum of
the first 25 terms of the series?
8. The sum of the first eight terms of an
arithmetic series is 176. The sum of the first
nine terms is 216. Determine the first and
ninth terms of the series.
9. The sum of the first n terms of an arithmetic
series is Sn = 3n2 + 4n.
a) Determine the first five partial sums.
b) Determine the first five terms of the
series.
c) Use the formula to verify that the sum of
the first five terms is equal to S5.
10. A student is offered the opportunity to earn
$6.00 for the first day, $11.00 for the second
day, $16.00 for the third day, and so on,
for 20 working days. Or, the student can
accept $1000 for the whole job. Which offer
pays more?
5. Determine the sum of each arithmetic series,
given the first and nth terms.
a) t1 = –3, t14 = 62
b) t1 =
3 , t10 = 18 3
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Name: ___________________________________________ Date: _____________________________
BLM 1–6
Section 1.3 Extra Practice
1. Is each sequence geometric? If it is, state the
common ratio and a formula to determine
the general term in the form tn = t1rn – 1.
a) 11, 33, 99, 297, …
b) 6, 12, 18, 24, …
1 2 4 8
c) , , , , …
3 3 3 3
d) 0.5, 0.2, 0.08, 0.032, …
2. Write the first four terms of each geometric
sequence.
a) t1 = 7, r = –3
1
b) t1 = –8, r =
2
n–1
c) tn = 3(0.6)
d) tn = (–4)n
3. Determine the number of terms in each
geometric sequence.
a) 4, 12, 36, " , 78 732
b) 5 2 , 10, 10 2 , " , 640
c) t1 = 5, r = −
1
5
, tn =
2
64
1
d) t1 = , r = 3, tn = 44 286.75
4
4. Determine the nth term of each geometric
sequence.
a) t1 = 2, r = 7
b) 6, –18, 54, –164, …
c) t1 = 7, t5 = 1792
1
1
d) r = , t8 =
4
4
5. Determine the unknown terms in each
geometric sequence.
a) 18, …, …, 6174
b) …, 4, …, …, 108
c) 5, …, …, …, 80
6. The first term of a geometric sequence is
0.1; the tenth term is 26 214.4. Determine
the value of the common ratio.
7. Determine the first term, the common ratio,
and an expression for the general term of
each geometric sequence.
a) t5 = 900, t7 = 0.09
b) t3 = –1728, t6 = 373 248
c) t5 = 28, t11 = 1792
d) t2 = 3, t4 = 0.75
8. The following sequences are geometric.
What is the value of each variable?
a) 8x – 12, 16, 64, 256, …
b) 25, 5, 1, 2y – 1, …
9. For a geometric sequence t4 = 4x + 8 and
1
t7 = x – 4. If the common ratio is , what is
2
the first term?
10. An excavating company has a digger that
was purchased for $240 000. It is
depreciating at 12% per year.
a) Determine the next three terms of this
geometric sequence.
b) Determine the general term. Define your
variables.
c) How much will the digger be worth in
7 years?
d) How long will it take before the
equipment is worth less than
$120 000?
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Name: ___________________________________________ Date: _____________________________
BLM 1–7
Section 1.4 Extra Practice
1. Determine whether each series is geometric.
Justify your answers.
a) 5 + 6 + 7.2 + 8.64 + …
b) 3125 – 625 + 125 – 25 + …
3 1 1 2
c) + + + +…
4 2 3 9
d) 2 + 3 + 5 + 8 + …
2. For each geometric series, state the
values of t1 and r. Then, determine each
partial sum.
a) 0.43 + 0.0043 + 0.000 043 + …, (S6)
b) 5 – 5 + 5 – …, (S10)
c) –100 + 50 – 25 + …, (S7)
3. Determine the partial sum, Sn, for each
geometric series described.
a) t1 = 50, r = 1.1, n = 4
b) t1 = –4, r = 2, n = 10
c) tn = (–5)(0.5)n – 1 , n = 5
d) tn = (3)(2)n – 1 , n = 12
4. Determine the partial sum, Sn, for each
geometric series.
a) 2 + 6 + 18 +
+ 354 294
b) t1 = –3, r = –2, tn = 6144
c) Sn = (–32)(0.75n – 1), n = 6
5. Determine the first term for each geometric
series.
a) Sn = 3932.4, tn = 4915.2, r = –4
b) Sn = 292 968, n = 8, r = 5
6. Determine the number of terms in each
geometric series.
a) 4 + 20 + 100 +
+ tn = 15 624
b) 1792 – 896 + 448 –
– tn = 1197
7. The fourth term of a geometric series is 30;
the ninth term is 960. Determine the sum of
the first nine terms.
8. The first term of a geometric sequence is 3.
The sum of the first two terms of the series is
15 and the sum of the first three terms of the
series is 63. Determine the common ratio.
9. Determine the first four terms of each
geometric series.
a) Sn = 5(3n – 1)
b) Sn = –24(0.5n – 1)
10. A ball is dropped from the top of a
25-m ladder. In each bounce, the ball
reaches a vertical height that is 3 the
5
previous vertical height. Determine the total
vertical distance travelled by the ball when
it contacts the ground for the sixth time.
Express your answer to the nearest tenth
of a metre.
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Name: ___________________________________________ Date: _____________________________
BLM 1–8
Section 1.5 Extra Practice
1. State whether each geometric series is
convergent or divergent.
5
a) 80 + 20 + 5 + + …
4
40
80
+
–…
b) –30 + 20 –
3
9
1
c) t1 = –5, r =
2
1
d) t1 = , r = –2
3
2. Determine the sum of each geometric series,
if it exists.
4
a) t1 = –4, r =
5
−2
b) t1 = 10, r =
3
c) 10 + 10 3 + 30 + 30 3 + …
d)
5
5
5
5
−
+
−
+…
3
9
27
81
2
3
3
⎛ −3 ⎞
⎛ −3 ⎞
⎛ −3 ⎞
f) – 2 – 2 ⎜ ⎟ – 2 ⎜ ⎟ – 2 ⎜ ⎟ – …
⎝ 4 ⎠
⎝ 4 ⎠
⎝ 4 ⎠
3. Express each of the following as an infinite
geometric series. Determine the sum of
the series.
a) 0.63
b) 7.45
5. The sum of an infinite geometric series is
10
and the first term is 5. Determine the
3
common ratio.
6. The sum of an infinite geometric series is
3π
1
and the common ratio is . Determine
2
2
the first term.
7. A ball is dropped from a height of 2.0 m
onto a floor. On each bounce the ball rises
to 75% of the height from which it fell.
Calculate the total distance the ball travels
before coming to rest.
8. Determine the values of x such that the
series 1 + x + x2 + x3 + … has a sum.
⎛2⎞
⎛2⎞
⎛2⎞
e) 8 + 8 ⎜ ⎟ + 8 ⎜ ⎟ + 8 ⎜ ⎟ + …
3
3
⎝ ⎠
⎝ ⎠
⎝3⎠
2
4. The general term of an infinite geometric
n −1
⎛1⎞
series is tn = 7 ⎜ ⎟ . Determine the sum of
⎝3⎠
the series, if it exists.
9. The sum of an infinite geometric series is
three times the first term. Determine the
common ratio.
10. A new oil well produces 12 000 m3/month
of oil. Its production is known to be
dropping by 2.5% each month.
a) What is the total production in the
first year?
b) Determine the total production of
the well.
c) 0.123 456
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Name: ___________________________________________ Date: _____________________________
BLM 1–9
Chapter 1 Test
Multiple Choice
For #1 to 5, select the best answer.
1. What are the missing terms of the arithmetic
sequence 4, …, 14, …, 24, …?
A
B
C
D
10, 20, 30
9, 19, 29
5, 10, 15
8, 18, 28
2. While baking a cake, Dylan notices that
each of his measuring cups is about half as
big as the one before it. The largest (first)
measuring cup is 250 mL. What is the
approximate capacity of the fourth
measuring cup?
A 125 mL
B 65 mL
C 30 mL
D 15 mL
3. The years in which the Commonwealth
Games take place form an arithmetic
sequence with a common difference of 4. In
1978, the Commonwealth Games were held
in Edmonton, Alberta. In which of the
following years could the Commonwealth
Games be held again?
A 2011
B 2022
C 2033
D 2044
4. The sum of the first 20 terms of the
arithmetic series 204 + 212 + 216 + ... is
A 11 200
B 7120
C 5680
D 5600
5. The sum of the first 11 terms of the
geometric series 7 – 14 + 28 – … is
A 28 679
B 4 781
C –9 555
D –28 665
Short Answer
6. Gentry notices that the bank of lockers
outside his math classroom are numbered
511, 513, 515, ..., 575. Determine the
number of lockers in the set.
7. Brittany, a landscape designer, is setting out
trees for planting. The 12 trees she needs are
currently in one location, 40 m from the
spot the first tree will be planted. The trees
will be spaced 6 m apart. The cart she uses
to transport the trees will only carry one tree
at a time, so she must take the first tree to its
spot, return for the second tree, take it to its
spot, and so on. After Brittany takes all
12 trees to the correct spot and returns to
the original location of the trees, how far
will she have travelled, in total?
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Name: ___________________________________________ Date: _____________________________
BLM 1–9
(continued)
8. Determine the sum of the arithmetic series
9 + 21 + 33 + " + 693.
9. In an arithmetic sequence, t3 = 16 and
t7 = 40.
a) Determine the common difference in the
sequence.
b) Determine the first term in the sequence.
c) Determine t100.
10. 5, …, 405 is a geometric sequence.
a) Determine all possible values for the
second term of this sequence.
b) Determine all possible general terms
for this sequence.
11. The nth sum of a sequence is given by the
formula Sn = 1 – 4n.
a) Determine the first three terms of the
sequence.
b) Decide whether the sequence is
arithmetic or geometric. Determine the
general term for the sequence.
Extended Response
12. Write a geometric series with a positive
first term.
a) Find the sum of the first ten terms of
your series.
b) Change the common ratio of your series
so the sum of the first ten terms is the
opposite sign, but the same value, as in
part a). For example, if your sum was
positive in part a), ensure that it is
negative for part b).
c) Create a geometric series so that Sn is
positive when n is odd, and Sn is negative
when n is even. Justify your answer.
13. According to Statistics Canada,
Chestermere, Alberta is one of the fastest
growing communities in Canada. Between
2001 and 2006, the population grew at an
average rate of about 8% per year.
a) The population of Chestermere in 2001
was 6462. Determine the population for
the years 2002 through 2004, inclusive.
b) Write the general term for the geometric
sequence that models the population of
Chestermere, where n is the number of
years starting in 2001.
c) Predict the population of Chestermere in
the year 2020.
d) What assumption(s) did you make in
your answer to part c)?
14. Write a sequence that is both arithmetic and
geometric.
a) Prove that your sequence is arithmetic.
Determine the general term of the
sequence.
b) Prove that your sequence is geometric.
Determine the general term of the
sequence.
c) How many sequences could be both
arithmetic and geometric? Justify your
answer.
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BLM 1–10
Chapter 1 BLM Answers
BLM 1–2 Chapter 1 Prerequisite Skills
b)
1. a) Non-linear. Each increase in the value of r
increases the value of A by a different amount
b) Linear. Each increase in the value of x increases
the value of y by the same amount, 5.
c) Non-linear. Each increase in the value of the first
coordinate increases the value of the second
coordinate by a different amount.
d) Linear. The same increase in the value of the first
coordinate (2) increases the value of the second
coordinate by the same amount, 5.
2. a)
Term Number
Value
1
9
2
16
3
23
4
30
5
37
b) v = 7t + 2 c) 499 d) t = 19
3. a)
Term Number
Value
1
−4
2
−9
3
−14
4
−19
−24
b) v = −5t + 1
Substitute t = 3. The result should be −14.
v = −5(3) + 1
v = −15 + 1
v = −14
c) −244 d) t = 18
4. a)
5
t=
1
s−2
3
4
⎛5⎞
5. a) y = −2x + 6 b) y = −3x − 9 c) y = − ⎜ ⎟ x +
3
⎝6⎠
3
d) y = 6x − 4 e) y = 7x + 9 f) y = 2 x −
4
1
4
or 0.0625 d)
6. a) 125 b) 1296 c)
16
9
1
2
7. a) −2 b) 3 c)
d) −
3
3
1
t3
4
8. a) 4 b) 2 c) 8t d) x6y30
12
s
9. a)
Number of
Amount of
2-min Intervals
Protactinium
0
1
1000
500
2
250
3
125
4
62.5
5
31.25
b) 12 min
BLM 1–3 Chapter 1 Warm-Up
y = 3x + 1
Section 1.1
1. a) The first term is 2. The common difference is 2.
b) The first term is 1. The common difference is 3.
c) The first term is 5. The common difference is 6.
2. a) x = 13 b) x = −29
3. a) g(1) = −5 b) g(0) = −11 c) g(−3) = −29
1
4. a) x = 19
b) x = 38
2
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BLM 1–10
(continued)
5. a) slope = 4, y-intercept = −1
b)
x
y
0
−1
1
3
2
7
3
11
4
15
5
19
Section 1.2
1. a) arithmetic sequence, t1 = 2, d = 2
b) not arithmetic sequence
c) arithmetic, t1 = 1, d = 3
d) arithmetic, t1 = −6, d = 5
2. a) tn is the general term, t1 is the first term, n is the
number of terms, and d is the common difference.
b) t26 = 78 c) t1 = −5 d) tn = 2 + 4(n – 1)
3. a) y = 6x b) y = 2x + 1 c) y = 18 + 36x
13
84
4. x = , y =
19
57
5. a)
b)
1
6
5. t1 = 7, r = 4, tn = 7(4) n – 1
4. a) r = 5 b) r =
Section 1.5
45
or –22.5
2
b) geometric, S18 = 6.0 c) arithmetic, S18 = 639
d) geometric, S18 = 3 145 716
1
2. a) t1 = 1, r = − and n = 11
3
n −1
1
⎛
⎞
b) tn = 1⎜ − ⎟
c) S11 = 0.75
⎝ 3⎠
1. a) arithmetic, S18 = −
3. a) 6, 3,
3 3 3
, ,
2 4 8
b) The length from A to G would be
3
cm or
16
0.1875 cm.
4. a) 0.2 b) 0.23 c) 0.047
27
343
5. a)
b) −
25
540
6. a) 0.06 b) 0.02 c) 0.00
BLM 1–4 Section 1.1 Extra Practice
Section 1.3
1. a) arithmetic, t1 = 2, d = 2
b) not arithmetic because you multiply by 2 to find
each successive term
c) arithmetic, t1 = 5, d = −2
1
to find
d) not arithmetic because you multiply by
2
each successive term
2. a) tn = 3n – 9 b) S10 = 75
3. a) 48 cm × 38.4 cm b) 15 cm × 12 cm
4. a) 3.56 b) 1.49 c) 1.51 d) s = 11.67
5. a) r = 27 b) r = 51.2
1. a) arithmetic; t1 = 4, d = 3; 16, 19, 22
b) arithmetic; t1 = 12, d = –5; –8, –13, –18
c) not arithmetic d) not arithmetic
e) arithmetic; t1 = x, d = 2; x + 8, x + 10, x + 12
2. a) –5, –7, –9, –11 b) 10, 9.5, 9, 8.5
c) 3, 3 + x, 3 + 2x, 3 + 3x d) 7 , 8 , 9 , 10
3 3 3 3
3. a) 10, 7, 4, 1
Section 1.4
1. a) neither b) arithmetic c) geometric
d) geometric e) arithmetic
2. a) r = –3; –54, 162; tn = 2(–3)n – 1
n −1
2 80 −160
⎛ −2 ⎞
,
b) r = − ;
; tn = 5 ⎜ ⎟
3 81 243
⎝ 3 ⎠
n–1
3. Solve 2(7)
= 4802 to get n = 5.
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BLM 1–10
(continued)
2. a) 7, –21, 63, –189
b) –8, –4, –2, –1
c) 3, 1.8, 1.08, 0.648
d) –4, 16, –64, 256
3. a) 10 b) 14 c) 7 d) 12
4. a) tn = 2(7)n – 1 b) tn = 6(–3) n – 1
n−1
⎛1⎞
c) tn = 7(4)n – 1 d) tn = 4096 ⎜ ⎟
⎝4⎠
b) 4 1 , 5, 5 1 , 6
2
2
5. a) 126, 882 b)
4
, 12, 36 c) ±10, 20, ±40
3
6. 4
7. a) t1 = 9 × 1010, r = ±0.01,
tn = (9 × 1010 )(±0.01)n – 1
b) t1 = –48, r = –6, tn = (–48)(–6)n – 1
c) t1 = 1.75, r = ±2, tn = (1.75)(±2) n – 1
d) t1 = ±6, r = ±0.5, tn = (6)(±0.5) n – 1
8. a) x = 2 b) y = 6 or 3
10
5
9. 384
10. a) $211 200, $185 856, $163 553
b) tn = 240 000(0.88) n – 1, tn = value of digger,
in dollars, n – 1 = years since purchase
c) $98 082 d) 6 years
4. a) tn = 4n + 2; t50 = 202 b) tn = 7 − 1 n ;
2 2
1
t50 = −21
2
5. a) 77 b) 26
6. a) 4, 8 , 12 , 16 b) 10 , 8, 6 , 4 , 2
c) 20, 14 , 8 , 2 , −4 , − 10
7. t1 = 12, tn = 5n + 7, t40 = 207
8. a) t1 = –15, d = 4, tn = 4n – 19
b) t1 = 93, d = –3, tn = 96 – 3n
10
25
23
9. x = ;
, 8,
3
3
3
10. a) 15, 18 b) tn = 3n + 3
c) 63 asterisks d) 41st diagram
BLM 1–7 Section 1.4 Extra Practice
BLM 1–5 Section 1.2 Extra Practice
1. a) –936 b) 232.5 c) 252.5 or 252
1
2
2. a) 378 b) 0 c) 400x
3. a) 15 b) 25 c) 21
4. a) t12 = –41, S12 = –228 b) t12 =
47
, S12 = 60
5
5. a) 413 b) 95 3
6. 71 071 7. 2850 8. t1 = 8, t9 = 40
9. a) S1 = 7, S2 = 20, S3 = 39, S4 = 64, S5 = 95
b) T1 = 7, T2 = 13, T3 = 19, T4 = 25, T5 = 31
c) S5 = 3(5)2 + 4(5) = 95
10. 6 + 11 + 16 + " + t20 = $1070. Therefore, the
arithmetic series method pays more money.
BLM 1–6 Section 1.3 Extra Practice
1. a) geometric, r = 3, tn = 11(3)n – 1
b) not geometric c) geometric, r = 2, tn =
d) geometric, r = 0.4, tn = (0.5)(0.4)n – 1
1 n–1
(2)
3
1. a) geometric series, the common ratio is 1.2
b) geometric series, the common ratio is –0.2
c) geometric series, the common ratio is 2
3
d) not geometric, no common ratio
2. a) t1 = 0.43, r = 0.01, S6 = 43
99
b) t1 = 5, r = –1, S10 = 0
c) t1 = –100, r = –0.5, S7 = −1075
16
−
155
3. a) 232.05 b) –4092 c)
d) 12 285
16
4. a) 531 440 b) 4095 c) 3367
128
5. a) 1.2 b) 3
6. a) 6 b) 9
7. 1916.25 8. 4
9. a) 10, 30, 90, 270 b) 12, 6, 3, 1.5
10. 94.2 m
BLM 1–8 Section 1.5 Extra Practice
1. a) convergent b) convergent c) convergent
d) divergent
5
8
2. a) –20 b) 6 c) does not exist d)
e) 24 f) −
4
7
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BLM 1–10
(continued)
63
63
63
7
+
+
+" =
2
3
100
11
(100)
(100)
5
5
5
41
b) 7.4 +
+
+
+"= 7
100 1000 10 000
90
c)
456
456
456
41 111
0.123 +
+
+
+" =
2
3
4
333 000
(1000)
(1000)
(1000)
3
21
1
4.
5. −
6. π 7. 14 m 8. |x| < 1
4
2
2
2
9.
10. a) 125 761 m3 b) 480 000 m3
3
3. a)
BLM 1–9 Chapter 1 Test
1. B 2. C 3. B 4. D 5. B
6. There are 33 lockers.
7. Brittany travelled 1752 m.
8. 20 358
9. a) d = 6 b) t1 = 4 c) t100 = 598
10. a) r = 9 or –9 b) tn = 5(9)n – 1 or tn = 5(–9)n – 1
11. a) –3, –12, –48
b) The sequence is geometric. tn = –3(4)n – 1
12. a) Example, for the series
2 + 10 + 50 + ..., S10 = 4 882 812.
b) Answers will vary. Students need to change the
sign of the first term, while leaving the common ratio
unchanged. In the example above, the series becomes
–2 – 10 – 50 – ..., S10 = 4 882 812.
c) Answers will vary. Correct answers must have
positive first term and negative common ratio.
For example, 2 – 10 + 50 – ….
13. a) 6979, 7537, 8140 b) tn = 6462(1.08)n – 1
c) 27 888
d) Answers will vary. For example, we assume that
population continues to grow at the same rate.
14. Answers will vary, however will all be in the
form k, k, k, …, where k is a real number.
a) Note that d = 0, so tn = k.
b) Note that r = 1, so tn = k.
c) There are infinitely many such sequences, but all
sequences will have the same form.
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